Integrand reduction of one-loop scattering amplitudes through Laurent series expansion

TL;DR

This paper introduces a semi-analytic integrand reduction method for one-loop scattering amplitudes using Laurent series expansion, simplifying the calculation of master integral coefficients.

Contribution

It develops a systematic Laurent expansion approach for integrand reduction, including cases with higher-rank numerators, enhancing computational efficiency and accuracy.

Findings

Coefficients are obtained by solving a diagonal system of equations.

The method handles numerators with rank larger than the number of propagators.

Implementation via polynomial division streamlines the reduction process.

Abstract

We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master integrals are the solutions of a diagonal system of equations, properly corrected by counterterms whose parametric form is konwn a priori. The Laurent expansion of the integrand is implemented through polynomial division. The extension of the integrand-reduction to the case of numerators with rank larger than the number of propagators is discussed as well.